Here’s the odd thing about bonds: the interest rate printed on one is frozen, but its price isn’t. When market rates move, bond prices move the other way.
This bond price calculator shows you exactly how. Give it the coupon, the time left and the yield that investors want today, and it tells you what the bond should sell for. It also reports the duration, a measure of how sharply that price reacts when rates change.
How to use the Bond Price Calculator#
- Enter the face value. What the bond repays at maturity.
- Enter the coupon rate. The fixed yearly interest as a percentage of face value.
- Enter the years to maturity. The time left until the bond is repaid.
- Enter the market yield. The yield investors demand for similar bonds today.
- Pick the coupon frequency. Most bonds pay twice a year.
- Read the result. You get the price, the premium or discount and the duration.
How a bond is priced#
A bond is worth the money it will pay you, valued in today’s terms. Each coupon and the final repayment is discounted back at the market yield, and the results are added together.
Here y is the yield per coupon period and N is the number of periods. If the market yield is higher than the coupon, the future payments are discounted harder and the price falls below face value. If it’s lower, the price rises above face value.
Price versus yield#
Take a bond with a face value of 1,000, a 5 percent coupon paid twice a year and 10 years to run. This is its price at different market yields:
| Market yield | Price | Status | Duration (years) |
|---|---|---|---|
| 3% | 1,171.69 | Premium | 8.17 |
| 4% | 1,081.76 | Premium | 8.08 |
| 5% | 1,000.00 | Par | 7.99 |
| 6% | 925.61 | Discount | 7.89 |
| 7% | 857.88 | Discount | 7.80 |
When the yield equals the coupon, the bond sells at exactly its face value. Push yields up from 4 to 5 percent and the price falls 7.56 percent, from 1,081.76 to 1,000.
What duration tells you#
Duration puts a number on how sensitive a bond’s price is to yield changes. The Macaulay duration is the average time, in years, until you get your money back, weighted by the size of each payment. The modified duration, shown by the calculator, turns that into a price sensitivity:
With a modified duration near 7.9, a one percentage point rise in yield cuts the price by roughly 7.9 percent. Longer bonds and lower coupons have higher durations, so they swing more. Long-term bonds are the ones that fall hard when rates rise, for exactly this reason.
Premium, discount and par#
Paying more than face value for a bond isn’t a mistake on its own. A bond with a coupon above current market yields is more attractive than newly issued ones, so it trades at a premium. You’re paid for that through the larger coupons, and the premium shrinks to nothing as the bond heads towards maturity. A discount bond works in reverse.
Limits of the calculator#
It prices the bond on a coupon date, so it leaves out accrued interest, which real markets add on top. It assumes the yield stays the same for the whole life of the bond, and that the bond can’t be repaid early. To go in the other direction and find the yield from a price you can see, use the bond calculator.
A worked bond example#
A bond with a face value of 1,000, a 6 percent coupon paid yearly and 5 years to maturity is priced at a market yield of 8 percent. The price is the present value of five coupons of 60 and the 1,000 face value, discounted at 8 percent. The sum comes to about 920.15, which is a discount to face value. If the market yield falls to 4 percent, the same bond is worth 1,089.04, a premium. When yields rise, prices fall, and the effect is bigger for bonds with a longer maturity.
Frequently asked questions#
Discount every coupon and the final repayment back at the market yield, then add them up. The calculator does this for you.
Newer bonds pay more, so older bonds with lower coupons must sell for less to give buyers the same yield.
It’s a bond that sells above its face value, usually because its coupon is higher than the current market yield.
Duration measures how sensitive a bond’s price is to changes in yield. A modified duration of 8 means about an 8 percent price change for each one percentage point move in yield.
Par value is the face value of a bond, the amount repaid at maturity. A bond trades at par when its price equals that amount.